if p(q) = q^2 4q- 12 then what is p(-1)

Answers

Answer 1
the solution:

(1): "q2" was replaced by "q^2".

Step by step solution :

STEP
1
:
Trying to factor by splitting the middle term

1.1 Factoring q2-4q-12

The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .

-12 + 1 = -11
-6 + 2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization

Equation at the end of step
1
:

(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : q+2 = 0

Subtract 2 from both sides of the equation :
q = -2

Solving a Single Variable Equation:

2.3 Solve : q-6 = 0

Add 6 to both sides of the equation :
q = 6

Supplement : Solving Quadratic Equation Directly

Solving q2-4q-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = q2-4q-12

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Aq2+Bq+C,the q -coordinate of the vertex is given by -B/(2A) . In our case the q coordinate is 2.0000

Plugging into the parabola formula 2.0000 for q we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 12.0
or y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
Vertex at {q,y} = { 2.00,-16.00}
q -Intercepts (Roots) :
Root 1 at {q,y} = {-2.00, 0.00}
Root 2 at {q,y} = { 6.00, 0.00}

Related Questions

Write an equivalent expression.

1. 8(y - 7)

2. -2x + 7

3. 3/5x + 2/5 + 3/5x

Answers

Answer:

8(y - 7) =8y-7-2x+7=7/2=3.5

The equivalent expressions are;

1. 8 (y - 7) = 8y - 56

2. - 2 (x + 7) = - 2x - 14

3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expressions are;

1. 8 (y - 7)

2. - 2 (x + 7)

3. 3/5x + 2/5 + 3/5x

Now,

Solve all the expression as;

1. 8 (y - 7) = 8 × y - 8 × 7

              = 8y - 56

Thus,  8 (y - 7) = 8y - 56

2. - 2 (x + 7) = - 2 × x - 2 × 7

                  = - 2x - 14

Thus, - 2 (x + 7) = - 2x - 14

3. 3/5x + 2/5 + 3/5x = 3/5x + 3/5x + 2/5

                              = (3x + 3x)/ 5 + 2/5

                              = 6x / 5 + 2/ 5

                              = (6x + 2) / 5

Thus, 3/5x + 2/5 + 3/5x = (6x + 2) / 5

Therefore, The equivalent expressions are;

1. 8 (y - 7) = 8y - 56

2. - 2 (x + 7) = - 2x - 14

3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5

Learn more about the expression visit:

https://brainly.com/question/25968875

#SPJ2

i need help... I cant figure This one out!! Lol someone help!

Answers

Answer:

x= 48

Step-by-step explanation:

x+90+42=180

x= 48

please mark brainliest

How many weeks will Sanjay need to ride his bike to work in order to ride 150 kilometers?

Answers

Answer:

This is because he rides 37.5 k/m every week. Multiply that by four and you get 150

Answer:

Sanjay will need to ride his bike to work for 4 weeks in order to ride 150 kilometers.

If you subtract 17 from my number and multiply the difference by ​-2, the result is ​-10." What is the ​number?

Answers

Answer:

22

Step-by-step explanation:

-10/-2 is 5

5+17 is 22

The roots of the equation 0 = x^3+ 2x^2– 3x are: _________.
These are the x-intercept values at these points: _________.

Answers

The answer is 1,0,-3

what is the least common denominator of 10 and 14​

Answers

Answer:

70

Step-by-step explanation:

Given -

the least common denominator of 10 and 14 is - *70*

Prime factor of 14 are 2 and 7

14 = 2 * 7

Prime factor of 10 are 2 * 5

10 = 2 * 5

Now Multiplying the highest exponent prime factor to calculate the LCM of 14 and 10

LCM (10,14) = 2 * 5 * 7

LCM (10,14) = 70

Hey guys, i need help on this one, thanks in advance.

Find the slope of the equation:

x - 5 = 3 ( y + 4 ) -2y + 1

if you could add step's please do.

Answers

Answer:

slope = 1

Step-by-step explanation:

1) expand those brackets on the left side my multiplying

x - 5 = 3y + 12 - 2y + 1

2) simplify by collecting like terms

x - 5 = y + 13

3) bring -5 to the right side by adding 5

x = y + 18

4) let's rearrange this equation in the form y = mx + c where m is the gradient (slope) and c is the y intercept. by subtracting 18 on both sides

y = (1)x - 18 (there is a 1 in front of the x, but we don't write it like that. m is 1)

y = x - 18

the slope is the gradient, which is 1

what is cosec32°/sec58°=

Answers

Answer:

1

Step-by-step explanation:

Using the cofunction identity

sec(90 - x) = cosecx , then

sec(90 - 58)° = cosec32° , so

[tex]\frac{cosec32}{sec58}[/tex]

= [tex]\frac{cosec32}{cosec32}[/tex]

= 1

Can you Explain your thinking.

Answers

Answer:

Record yourself explaining your thoughts and listen to the recording. Continue re-recording what you say and listening to your recording until it sounds they way you want it to.

What is the slope of the line that passes through the points (5, 6)(5,6) and (5, 9) ?(5,9)? Write your answer in simplest form.

Answers

Answer:

The slope is undefined.

Step-by-step explanation:

You can use slope formula (y - y)/(x - x) and you will get a zero on the bottom (never allowed) OR notice that the x's are the same so sketch a graph, the line is vertical...that means that slope is undefined.

there is a proportional relationship between x and y. complete the table with the missing values

Answers

Answer:

I think you forgot to attach the table

if r and s represent the solutions of the equation below and r>s, what is the value of the difference r-s?

(3x+14)x=5

Answers

Answer:

16/3

Step-by-step explanation:

(3x + 14)x = 5

3x² + 14x = 5

3x² + 14x - 5 = 0

3x² + 15x - x - 5 = 0

3x(x + 5) - 1(x + 5) = 0

(3x - 1)(x + 5) = 0

x = 1/3 & -5

Here,

r = 1/3

s = -5

r - s

1/3 - (-5)

1/3 + 5

1 + 15/3

16/3

the value of the difference r-s is [tex]\bold{\frac{16}{3}}[/tex]

Answer:

Solution given:

(3x+14)x=5

opening bracket

3x²+14x=5

3x²+14x-5=0

Doing middle term factorisation

3x²+(15-1)x-5=0

3x²+15x-x-5=0

3x(x+5)-1(x+5)=0

(3x-1)(x+5)=0

either

x=-5

or

3x-1=0

3x=1

x=⅓

According to question value of x is r>s

so

⅓>-5

so

r=⅓

and

s=-5

Now

r-s=-(-5)=[tex]\frac{1+5*3}{3}=\frac{16}{3}[/tex]

You can answer the ones you want to. At least one.


Have no idea how to do this. Please help I beg you.

Answers

Answer:

Step-by-step explanation:

5a.) It starts with two at time one and increases by one each time

5b.) x+1

6.) Formula: (2/3)(x-1)+1, the fifth term would be (2/3)*(5-1)+1= 11/3

7a.) I will leave you to make the table. n+2 is wrong because it's increasing by 2 blocks each time

7b.) 2n+1

8a.) x²

8b.) just draw a 6x6

8c.) 12²=144

Solve for x. Round your answer to the nearest tenth if necessary.
70°
6
X

Answers

Answer:

Tan 70 = opp/adj

Tan 70 = x/6

multiply by 6 on both sides

16.5 = x

Evaluate -(2-6)(23).
O A. -8
B.
1/8
C. 8
O D.
- 1 / 8

Answers

Answer:

92

Step-by-step explanation:

- ( 2 - 6 )

= - ( - 4 )

= 4

- ( 2 - 6 ) ( 23 )

= 4 x 23

= 92

The evaluation of  - (2- 6) ( 23) is 92

In mathematics, evaluation is a systematic method used in solving expressions. From the given information, we need to first solve the expressions in the brackets before multiplying them together.

From the given information:

= - ( 2 - 6) (23)

= - ( -4) (23)

= 4 × 23

= 92

Learn more about how to evaluate in mathematics here:

https://brainly.com/question/10426112

What’s 10^102????????€

Answers

Answer:

(2^102•5^102)

Step-by-step explanation:

(10)^102 = (2•5)^102 = 2^102 • 5^102

An ice cream shop sells ice cream cones, c, and
milkshakes, m. Each ice cream cone costs $1.50
and each milkshake costs $2.00. Donna has $19.00
to spend on ice cream cones and milkshakes. If she
must buy 5 ice cream cones, which inequality could
be used to determine the maximum number of
milkshakes she can buy?

Answers

Answer:

$7.50+m > $19

The inequality to be used for determining the maximum number of milkshakes she can buy will be in the form of:

[tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]

  The inequality in the position or the relationship between two variables in order to make the total either greater than, less than, or greater than equal to, or less than equal to the total amount.  

The inequality can be between numbers or algebraic expressions.  

In the given case,

Per unit cost of ice cream cone $1.50 Per unit cost of milkshakes $2.00 The total amount for spending is $19.00 Number of ice cream cones bought 5  

To determine the inequality for the number of milkshakes the inequality will be formed as follows:  

The total cost of ice cream cones will be added with the total cost of milkshakes (where m is the number of milkshakes) and the sign used will be greater than or equal to the given amount to be spent.  

Therefore, the inequality will be  [tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]

  To know more about inequality, refer to the link:

https://brainly.com/question/11897796    

Researchers claim that 90% of people are left handed. Suppose the researchers' claim is true. Mrs. Reyes has a Statistics class with 30 students. What is the probability that exactly 25 of them are left handed?

Answers

Answer:

10.23% to the nearest hundredth.

Step-by-step explanation:

This is a Binomial Probability Distribution.

If exactly 25 are left handed then exactly 5 are right handed.

So (probability that exactly 25 are left handed)

= 30C5*(0.1)^5(0.9)^25

= 0.1023047706

= 10.23%.

The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem involves the binomial probability distribution, where we have a fixed number of trials (30 students in this case), and each trial has two possible outcomes (left-handed or not left-handed).

The probability of success (a student being left-handed) is 0.9, based on the researchers' claim.

The probability of a failure (a student not being left-handed) is 1 - 0.9 = 0.1.

We want to find the probability that exactly 25 students out of 30 are left-handed.

This can be calculated using the binomial probability formula:

[tex]P(X = k) = ^nC_ kp^k (1 - p)^{n-k}[/tex]

where:

n = 30 (the number of trials)

k = 25 (the number of successes we want)

p = 0.9 (the probability of success in each trial)

Plugging in the values, we get:

[tex]P(X = 25) = ^{30}C_ {25}~ 0.9^{25} ~0.1^5[/tex]

Using a calculator or statistical software, we can find that:

P(X = 25) ≈ 0.2031

Therefore,

The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ2

Find the missing factor

Answers

Answer:

[tex](x^4y^5)(x^2y^4)[/tex]

Step-by-step explanation:

Keep these things in mind:

[tex]x^3\times x^3=x^{3+3}=x^6\\\\(x^3)^3=x^{3\times3}=x^9[/tex]

Using those, simplify the left side of this equation:

[tex](x^2y^3)^3\\x^6y^9[/tex]

Now we know what the exponents need to become, so we can find the difference between those and what we have on the right:

[tex]6-4=2\\9-5=4[/tex]

We need to add a 2 to the x, and add a 4 to the y.

[tex](x^4y^5)(x^2y^4)[/tex]

80 as the product of it prime factors in ascending order

Answers

Answer:

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Prime Factorization of 80: 80 = 24 × 5.

Step-by-step explanation:

Answer:

This is true

Step-by-step explanation:

This is true because of the communitive property that makes the numbers you multiply the same product in different orders

Tell whether each equation has one, zero, or infinitely many solutions.
Solve the equation if it has one solution.



4x + 2 = x + 8 PLZZZZZ

Answers

Answer:

Exactly One Solution

Step-by-step explanation:

4x + 2 = x + 8

3x = 6                Simplify.

x = 2                  Divide by 2.

Answer:

One solution, x = 2

Step-by-step explanation:

4x + 2 = x + 8 (Given)

4x = x + 6

(The 2 is subtracted from the right side, therefore the left side is also subtracted. 8 becomes 6.)

3x = 6

(The x is subtracted from the right side to the left side. Thus turning the 4x into 3x)

x = 2

(The 3 is divided out to get x alone. So, the 6 has to be divided by 3 as well, turning it into 2)

questions
124 - 444 = ...
345 - (-7) × (-6) = ...​

Answers

Answer:

-320; 303

Step-by-step explanation:

Well... you could really just use a calculator to do this, I mean?

124 - 444 = -320

345 - (-7)*(-6) = 345 - 42 = 303

Answer:

1) 320

2) 303

Step-by-step explanation:

1) simple Subtraction

2) first multiply -7 & -6 = 42

then 345-42 = 303

I need answers to these questions

Answers

Answer is in the attached file...

!!!!!!!!!!!!!!determine which of these are perpendicular parallel or none

Answers

Line A and B are perpendicular and Line A and C are parallel

Answer:

Parallel: a and c

Perpendicular: a and b, c and b

Step-by-step explanation:

Basically you would want to isolate for y.

Line a:

4y - 12x = 20

4y = 12x  + 20

y = 12x/4 + 20/4

y = 3x + 5

Line b:

3y = -x+2

y = -x/3 + 2/3

Line c:

y=3x - 1

Now look at each line and compare their slopes.

-Lines a and c have same slope., thus they are parallel.

-lines a and b are perpendicular because the slopes are negative reciprocals each other

-lines b and c are also perpendicular

what is the slope of the line that goes through 11,2 and 14,16

Answers

Step-by-step explanation:

m = y2-y1/x2-x1

m = 16 - 2/ 14 - 11

m = 14/3

m = 14 / 3

Hope it helps.

Sally is paid to walk her neighbor’s dog every day.Every month she is paid she puts away $20 and saves the rest.Write an expression that represents the amount she will save in 6 months if she earns m dollars each month.If she’s paid $65 each month how much will she save in 6 months?

Answers

Answer: she would have saved 120$$

Step-by-step explanation:

Show Work to factor the binomials.

Answers

[tex](14)\\\\x^2 + 14x +45\\\\=x^2 +5x +9x +45\\\\=x(x+5) +9(x+5)\\\\=(x+9)(x+5)\\\\(15)\\\\x^2 +18x +45\\\\=x^2 +15x +3x +45\\\\= x(x+15) +3(x+15)\\\\=(x+3)(x+15)\\\\\\(16)\\\\x^2+46x+45\\\\=x^2 +45x +x +45\\\\=x(x+45) +(x+45)\\\\=(x+45)(x+1)[/tex]

is zero a rational number?​

Answers

Yes 0 is a rational number

Answer:

yes

Step-by-step explanation:

we know that every integer is a rational number and Zero can be represented as the ratio of two integers.

if x and y are positive numbers xy = 96 what is the value of x

Answers

The value of x is 96/y where y is not equal to zero.

Given the expression that relates x and y as xy = 96

We are told that x and y are positive numbers. To get the value of x, we will divide both sides by y as shown:

[tex]xy = 96\\\frac{xy}{y} =\frac{96}{y} \\x = \frac{96}{y} \\[/tex]

From the result, we can conclude that the value of x is 96/y where y is not equal to zero.

Learn more on functions here: https://brainly.com/question/17431959

Pls due tmr pls pls fast I need it like rn

Answers

Answer:

Step-by-step explanation:

50 of 100

= 50%

120 of 1

= 1.2%

Other Questions
Cruse was made a slave for two years but he never stops scouting foreign lands and oceans discuss the validity of this statement taking into consideration the notion of colonialism. 1. What impact did Napoleonic Europe have on neighboring countries of France? The Supreme Court CANNOT rule a law unconstitutional if it has been approved by thepresident.True or false (b) A sum of money was to be shared among three friends Keisha, Tracey, and Kerry-Ann, in theratio 7:9:11 respectively. If Kerry-Ann received $3,300.00, find the sum of money that wasbetween the three friends. 2. ustedes / al lado / puertawhat would this be in a sentence Can someone help me fill out the pictures I havent done (LINKS WILL BE REPORTED) Find the sum of the first 20 terms of the sequence 2, 8, 14, 20, . . .. What is the answer step by step explanation please.w (3w + 2) + 5w I'm currently reading the book "the pearl" my teacher asked some questions on it and these few ones I'm not quite sure how to answer. I do not have a book with me and this assignment is tomorrow.In chapter 4 kino is attacked for the second time describe this attack. What phrase does Kino repeat to convince Juana that hes making the right decision in chapter 4? How do ecosystems function? (Select all that apply.) Biotic factors depend on each other for food, shelter, protection, and reproduction. Biotic factors are dependent on abiotic factors for food and protection. Abiotic factors depend on biotic factors for food, shelter, protection, and reproduction. Abiotic factors affect the type and number of organisms that live in a particular ecosystem. What were the political and social effects of westward migration in the early 19th century? In a ________ drainage pattern that is generally developed in areas underlain by a fairly symmetrical mountain, such as a volcano. Which Hindu god became part elephant? based on your answer in part A what role does gravity play in the separation of the liquids shown When are you old enough to ask your parents to go out of state (by yourself or with a group of friends). For example, for a convention Please help and explain when the moon appears to completely cover the sun, the moon must be at which phase? HELP PLEASE!! ;-; !! TWO PART QUESTION!! 1) Consider the image. Are the two triangles congruent if a is congruent to d and b is congruent to e?A) Yes, by the ASA postulate.B) Yes, by the SAS postulate.Yes, by the SSS postulate.D) No, they are not congruent.2) suppose that three corresponding angles are congruent for two triangles (AAA), why cant congruence be proved between the two triangles?A) the triangles could have the same shape but not the same size.B) The triangles could have the same size but not the same shape. C) with three equal angles, only the shortest side of the triangles can be congruent.D)With three equal angles, only the longest side of the triangles can be congruent. Consider a property with NOI of $72,000 and a debt coverage ratio of 1.2 applied to first year NOI. What would be the estimated monthly mortgage payment A coin of mass 0.0050 kg is placed on a horizontal disk at a distance of 0.14 m from the center, as shown above. The coin doesnt slip and the time it takes for the coin to make a complete revolution is 1.5 s. A)The figure below shows the disk and coin as viewed from above. Draw and label vectors on the figure below to show instantaneous acceleration and linear velocity vectors for the pin when it is at the position shown below.B)Determine the linear speed of the coinC)The rate of rotation of the disk is gradually increased. The coefficient of stats if friction between the coin and the disk is 0.50. Determine the linear speed of the coin when it just begins to slip. D)If the experiment in part c were repeated with a second, identical coin glued to the top of the first coin, how would this affect the answer to part c? Explain.